[1]}, building on work in, e.g., [2]}, argue that the so-called SafeBayes algorithm will select a learning rate \(\eta \)  that is sufficiently small in the sense above. Define the cumulative expected log-loss under the \(\eta \) -generalized Bayes posterior distribution, as a function of \(\eta \) :
\( \eta \mapsto \sum _{i=1}^n \int -\log p_\theta (Y_i \mid X_i) \, \Pi _{i-1}^{(\eta )}(d\theta ). \) 
